SFB 
823 
A cointegrating polynomial 
regression analysis of the 
material Kuznets curve 
hypothesis 
D
iscussion P
aper 
 
Manuel Frondel, Peter Grabarczyk, 
Stephan Sommer, Martin Wagner 
 
 
Nr. 72/2016 
 
 
 
 
 
 
 
 
 
A Cointegrating Polynomial Regression Analysis
of the Material Kuznets Curve Hypothesis
Manuel Frondel∗, Peter Grabarczyk†, Stephan Sommer‡, Martin Wagner§
Employing consumption data for aluminum, lead and zinc for eight OECD coun-
tries spanning from 1900 to 2006, this paper tests the hypothesis underlying the no-
tion of the Material Kuznets Curve (MKC), which postulates an inverted U-shaped
relationship between a country’s level of economic development and its intensity
of metal use. Applying the tests and estimation techniques for nonlinear cointe-
gration developed by Saikkonen and Choi (2004), Wagner (2013) as well as Wagner
and Hong (2016), we find that the MKC hypothesis is less strongly supported by
the data than when employing the standard methods that have been used in the
empirical Environmental Kuznets Curve (EKC) literature so far. The evidence for a
cointegrating MKC is mixed, at best.
Keywords: Intensity of Use, Metals, Nonlinear Cointegration.
JEL codes: C12, C13, C22, Q32.
Acknowledgements: We gratefully acknowledge financial support by the Collaborative Research
Center “Statistical Modelling of Nonlinear Dynamic Processes” (SFB 823) of the German Re-
search Foundation (DFG), within Project A3, “Dynamic Technology Modelling”. The usual
disclaimer applies.
1 Introduction
Investigating the nexus between economic growth and environmental degradation, caused
for example by the emission of greenhouse gases and other pollutants, has been at the heart
of a great deal of empirical studies. Inspired by the seminal work of Grossman and Krueger
(1991, 1995), as well as Holtz-Eakin and Selden (1995), a prominent topic of this strand of the
literature is the so-called Environmental Kuznets Curve (EKC) hypothesis,1 postulating an in-
verted U-shaped relationship between a country’s economic activity, typically measured by
∗RWI – Leibniz Institute for Economic Research.
†Technical University Dortmund
‡RWI – Leibniz Institute for Economic Research.
§Technical University Dortmund, Institute for Advanced Studies, Vienna, and Bank of Slovenia, Ljubljana.
1The term EKC hypothesis was coined in analogy to the inverted U-shaped relationship between the level of
economic development and the degree of income inequality that was postulated by Kuznets (1955) in his presi-
dential address to the American Economic Association.
1
Table 1: Overview on Selected Recent Studies on the MKC Hypothesis
Estimation Unit Root Cointegration Support of
Methods Tests Tests MKC Hypothesis
Bringezu et al. (2004) OLS, FGLS,
FE, RE
– – Yes
Canas et al. (2003) OLS, FE, RE – – Yes
Crompton (2015) FE Pesaran, Im-Pesaran-Shin, Choi – Yes
Focacci (2005) OLS – – No
Guzma´n et al. (2005) FGLS, NLLS Augmented Dickey-Fuller test Augmented Dickey-Fuller Yes
Huh (2011) VECM, VAR Augmented Dickey-Fuller,
Philips-Perron
Johansen cointegration
likelihood ratio
Yes
Jaunky (2012) GMM, VECM Augmented Dickey-Fuller,
Zivot-Andrews, Narayan-Popp,
Levin-Lin-Chu,
Im-Pesaran-Shin, Pesaran,
Chang-Song
Nyblom-Harvey, Pedroni,
Westerlund
Yes
Jaunky (2013) VECM Augmented Dickey-Fuller,
Zivot-Andrews, Narayan-Popp,
Levin-Lin-Chu,
Im-Pesaran-Shin, Pesaran,
Chang-Song
Pedroni, Westerlund,
Westerlund-Edgerton, Di
Iorio-Fachin
Yes
Wa˚rell (2014) OLS, FE Pesaran Westerlund for
middle-income
countries
Note: FE: Fixed Effects, FGLS: Feasible Generalized Least Squares, GMM: Generalized Methods-of-Moments, NLLS:
Non-Linear Least Squares, OLS: Ordinary Least Squares, RE: Random Effects, VAR: Vector Autoregression Model, VECM:
Vector Error Correction Model.
gross domestic product (GDP) per capita, and per-capita measures of various kinds of pollu-
tants as dependent variables. In econometric terms, the hypothesized inverted U-shape of this
relationship requires that in addition to (log) GDP per capita, we must include the square of
this explanatory variable, and maybe also higher powers, in any specification employed to test
the EKC hypothesis.
The reasoning underlying such specifications and the EKC hypothesis is that in early stages
of economic development, environmental degradation and pollution increase with economic
development, but beyond some welfare level the positive trend reverses and further economic
growth may lead to environmental improvement (Stern, 2004). This level may vary for both
countries and environmental indicators.
A similar reasoning is adopted for the nexus between economic development and the use of
materials, for which Focacci (2005) coined the notion Material Kuznets Curve (MKC). While
2
Malenbaum (1978) was the first to analyze the MKC hypothesis for a large set of metals, this
strand of the literature enjoys growing popularity – see Table 1 for recent examples and its con-
tinuation in Table A.1 in the appendix. In line with large parts of the empirical EKC literature,
the table shows that some MKC studies do not use unit-root and cointegration techniques at
all. Equally disconcerting is that those studies that employ unit-root and cointegration tests,
use linear, rather than nonlinear techniques, thereby ignoring the fact that powers of an inte-
grated process, e.g. log GDP per capita, are not integrated processes of any order – for more
details on this fact see Mu¨ller-Fu¨rstenberger and Wagner (2007) and Wagner (2008, 2012). To
prevent misplaced conclusions with respect to the existence of an MKC, both unit-root and
cointegration tests, as well as cointegration estimation techniques, need to be modified to suit
to the, in the words of Wagner and Hong (2016), cointegrating polynomial regression (CPR) con-
text, thereby accounting for the fact that the MKC hypothesis necessitates powers of economic
indicators as regressors.2
By applying the cointegration tests of Wagner (2013), together with estimation techniques
from Saikkonen and Choi (2004) as well as Wagner and Hong (2016), and employing metal
use data spanning from about 1900 to 2006 for aluminum, lead and zinc, this paper tests the
MKC hypothesis between a country’s GDP per capita and the ratio of metal consumption to
GDP (intensity of use, IOU) for eight OECD countries, including highly industrialized coun-
tries such as the US, Japan, and Germany. Our empirical analysis demonstrates that, similar to
the conclusions drawn from the EKC analysis by Wagner (2015), the evidence for a MKC re-
lationship is strongly diminished compared to that resulting from applying standard tests for
linear cointegration. In those cases in which the MKC hypothesis cannot be rejected, we find
the expected inverted-U-shaped relationship between log per-capita GDP and log intensity of
use for the majority of this subset of countries.
The subsequent section describes the data used for our analysis, while Section 3 discusses
the empirical results. The final section summarizes and concludes.
2 Data and MKC Hypothesis
It is well known that long time series are beneficial for valid estimation and inference in
cointegration analysis. As a consequence, when empirically analyzing the nexus between a
2In terms of econometric analysis, the present paper is similar in scope for the empirical MKC literature as Wagner
(2015) for the empirical EKC literature.
3
country’s economic development and its metal use, long time series for these variables are
required. Consequently, data availability is a crucial determinant of both the depth and width
of any such analysis. While exploiting data on metal use from a variety of sources, such as the
World Bureau of Metal Statistics (WBMS), we have opted for making use of the longest time
series on metal use, which are available for aluminum, lead, and zinc for eight OECD countries:
Australia, France, Germany, Italy, Japan, Switzerland, UK and the US – for an overview on the
available data, see Table A.2 in the appendix.
In addition, any investigation of the MKC hypothesis necessitates data on a country’s eco-
nomic performance. To this end, data on GDP per capita is retrieved from the so-called Mad-
dison Project and measured in Geary-Khamis Dollar (henceforth abbreviated by $) with base
year 1990 (Bolt and Zanden, 2014).
A casual inspection of Figures 1 to 3 on the existence of a MKC yields some substance in
the case of aluminum for countries such as Australia, France and USA. The MKC hypothesis
appears to fit even better for lead, for which consumption declines for the majority of these
countries upon reaching fairly low individual threshold values. This decline, however, may be
due to the fact that the toxic character of lead eventually forced these countries to reduce their
lead use. Although a similar explanation does not apply to zinc, its consumption per unit of
GDP shrank in all countries alongside with increasing GDP per capita.
Figure 1: Log Aluminum Use per GDP (in metric tons per million $) versus Log GDP per Capita (in
1990$)
-6
-4
-2
0
Lo
g 
al
um
in
iu
m
 c
on
su
m
pt
io
n 
pe
r m
ill
io
n 
$ 
of
 G
D
P
 (m
et
ric
 t)
7 8 9 10 11
Log GDP per capita in 1990 $
Australia France Germany Italy
Japan Switzerland USA UK
4
Figure 2: Log Lead Use per GDP (in metric tons per million $) versus Log GDP per Capita (in 1990 $)
-4
-3
-2
-1
0
Lo
g 
le
ad
 c
on
su
m
pt
io
n 
pe
r m
ill
io
n 
$ 
of
 G
D
P
 (m
et
ric
 t)
7 8 9 10 11
Log GDP per capita in 1990 $
Australia France Germany Italy
Japan Switzerland USA UK
Figure 3: Log Zinc Use per GDP (in metric tons per million $) versus Log GDP per Capita (in 1990$)
-5
-4
-3
-2
-1
0
Lo
g 
zi
nc
 c
on
su
m
pt
io
n 
pe
r m
ill
io
n 
$ 
of
 G
D
P
 (m
et
ric
 t)
7 8 9 10 11
Log GDP per capita in 1990 $
Australia France Germany Italy
Japan Switzerland USA UK
5
These figures suggest that a quadratic specification of the MKC hypothesis
mt = c + δ · t + β1 · yt + β2 · y2t + ut, (1)
may suffice. Here mt denotes the natural logarithm of the intensity of use of metal m in year
t, measured in metric tons per million Geary-Khamis $, yt denotes log GDP per capita, t is a
linear time trend, ut denotes the error term and c, δ, β1 as well as β2 are the parameters to be
estimated. The hypothesis of an inverted U-shaped MKC requires β1 to be positive and β2
to be negative. Apart from the time trend, Equation 1 is the usual quadratic equation used
for studying the MKC hypothesis (Jaunky, 2012, p. 298). Based on Equation 1, the per-capita
GDP value of the turning point from which on the intensity of metal use shrinks is given by
exp
(
− β12β2
)
.
Inspired by Figures 1 - 3, which suggest country-specific MKCs with individual turning
points, we have opted for individually analyzing the MKC hypothesis for each country, thereby
refraining from the use of panel data estimators. Among other assumptions, their application
would impose the restriction that all countries exhibit the same income elasticity at any given
income level (Stern, 2004).
3 Empirical Analysis
Since the seminal work of Granger and Newbold (1974), researchers increasingly pay atten-
tion to the unit root properties of macroeconomic time series, such as GDP and resource con-
sumption. These variables are frequently found to be integrated of order one (I(1)). Hence,
before assessing the existence of any nexus between metal use and economic growth, it is im-
perative to individually test for each country (i) whether (log) GDP per capita is an I(1) process
using unit-root tests and, if this holds true, (ii) whether the error term in Equation 1 is station-
ary using, e.g., tests for nonlinear cointegration developed by Wagner (2013) and Wagner and
Hong (2016), rather than standard cointegration tests. In contrast to these tests for nonlinear
cointegration, classical cointegration tests are based on the assumption that all stochastic re-
gressors appearing in Equation 1, i. e. yt and y2t , as well as the dependent variable mt, are I(1).
It is, however, known (see, e.g., Wagner, 2012) that yt being I(1) implies that y2t cannot be I(1);
and is in fact not integrated of any integer order.
6
Table 2: Test Statistics of the Phillips-Perron (PP) and the Augmented Dickey-Fuller (ADF) Unit-Root
Test for log GDP per capita (yt)
Intercept and
Intercept linear trend
PP ADF PP ADF
Australia 0.67 2.73 -2.02 -1.57
France -0.14 0.77 -2.38 -1.71
Germany -0.41 0.59 -2.76 -2.56
Italy -0.19 1.39 -1.76 -1.87
Japan 0.01 1.53 -1.89 -1.30
Switzerland -0.43 1.63 -1.91 -1.77
USA -0.28 2.01 -3.14 -2.95
UK 1.37 1.34 -2.17 -0.50
Note: Bartlett kernel and Newey and West (1994) bandwidth for long-run covariance estimation. The optimal number of
lags for the ADF test is based on the sequential t method (Ng and Perron, 1995), but it is omitted for the sake of expositional
simplicity. Asterisks * and ** indicate rejection of the null hypothesis at the 10% and 5% significance level, respectively.
3.1 Unit Root Tests
Applying both the unit-root test of Phillips and Perron (1988) and the Augmented Dickey-
Fuller (ADF) test of Dickey and Fuller (1981) to log GDP per capita (yt), the null hypothesis of
yt being I(1) cannot be rejected throughout (Table 2). In what follows, we therefore employ
cointegration tests, that is, we examine the stationarity of the error term in Equation 1. Due
to the above mentioned fact that powers of an integrated process, such as log GDP per capita,
are not integrated processes of any order, testing whether Equation 1 is a cointegrating rela-
tionship requires modified tests for a cointegrating polynomial regression setting, which have
not been applied in the MKC literature so far. These tests, applied in the following section, are
modifications of the (non-)cointegration test of Phillips and Ouliaris (1990) and the cointegra-
tion test of Shin (1994) to investigate cointegration in a polynomial regression setting, such as
that underlying the MKC hypothesis.
3.2 Cointegration Tests
To test whether Equation 1 is a cointegrating polynomial relationship, we use the tests de-
veloped by Wagner (2013) and Wagner and Hong (2016). First, we employ the extension of the
non-cointegration test of Phillips and Ouliaris (1990) to cointegrating polynomial regressions
(CPRs) of Wagner (2013), denoted here by Puˆ. Second, we use a cointegration test for CPRs,
denoted here by CT, with the flipped null hypothesis of cointegration discussed in Wagner
7
Table 3: Results of the Puˆ Non-Cointegration Test and the CT Cointegration Test
Aluminum Lead Zinc
Puˆ CT Puˆ CT Puˆ CT
Australia 49.97* 0.10* 49.56* 0.05 16.67 0.08
France 12.18 0.07 61.03** 0.07 81.11** 0.05
Germany 57.71** 0.11** 67.88** 0.07 74.76** 0.06
Italy 34.81 0.08 41.13 0.04 51.17* 0.05
Japan 53.61** 0.07 34.97 0.12** 29.45 0.07
Switzerland 61.13** 0.06 70.20** 0.06 62.42** 0.06
USA 30.52 0.05 55.06** 0.09* 52.82* 0.09*
United Kingdom 11.72 0.09* 37.32 0.05 43.86 0.06
Bartlett kernel and Newey and West (1994) bandwidth for long-run covariance estimation. Asterisks * and **
indicate rejection of the null hypothesis at the 10% and 5% significance level, respectively.
and Hong (2016).3
Table 3 presents the results based on the Puˆ non-cointegration test and the CT cointegration
test. For aluminum, the combined evidence originating from both tests suggests that only for
Japan and Switzerland there may be a cointegrating MKC. For these two countries, the Puˆ test
rejects the null and the CT test does not reject the null. With respect to lead, the MKC hypoth-
esis is supported for four countries (Australia, France, Germany, and Switzerland), while in
case of zinc there is statistical support France, Germany, Italy and Switzerland.
In addition, for comparative purposes, we have also applied the Phillips and Ouliaris (1990)
non-cointegration test and the Shin (1994) cointegration test, with the results reported in Ta-
ble A.3 in the appendix. The results obtained from these tests for the null hypothesis of linear
cointegration respectively the absence of linear cointegration lead to seemingly stronger evi-
dence of the MKC hypothesis than the CPR evidence reported here. This is a similar finding
to Wagner (2015), who also finds “too strong” evidence for the prevalence of an EKC (for CO2
and SO2 emissions) when using inappropriate tests.
3The CT test uses critical values that differ from those of the Shin (1994) test and that depend upon the specification
of the deterministic component, the number of integrated regressors and the included powers of the integrated
regressors. In case of only a single integrated regressor present in the regression with powers larger than one
as given in Equation 1, the limiting distribution is nuisance parameter free. The Puˆ non-cointegration test is
an extension of the variance-ratio test of Phillips and Ouliaris (1990) and involves a long-run variance estimate
based on the residual of a VAR(1) regression for [mt, yt]′ including deterministic components, see Wagner (2013)
for more details.
8
3.3 Estimation Results
For the countries with evidence of a cointegrating MKC relationship, we next estimate Equa-
tion 1. To allow for asymptotic standard inference, the OLS estimator, consistent in the coin-
tegration case despite regressor endogeneity and error serial correlation, needs to be suitably
modified. The literature provides several such modifications originally considered for lin-
ear cointegrating relationships: the Fully Modified OLS (FM-OLS) estimator of Phillips and
Hansen (1990), the dynamic OLS (D-OLS) estimator of Saikkonen (1991) or the Integrated
Modified OLS estimator of Vogelsang and Wagner (2014). The FM-OLS approach rests upon a
two-step transformation: first, the dependent variable is modified to wipe out the dependence
of the error term ut on the errors that generate the integrated regressors. Second, an addi-
tive bias term is removed by a suitable additive correction factor. The dynamic OLS (D-OLS)
approach as suggested by Saikkonen (1991) tackles the nuisance parameter dependencies of
the OLS limiting distribution via augmenting the regression by leads and lags of the first dif-
ferences of the integrated regressor. These estimation approaches have been extended for the
CPR context by, e.g., Wagner and Hong (2016) for the FM-OLS estimator and Saikkonen and
Choi (2004) for the D-OLS estimator.4 In the following tables, we label these extended estima-
tors by FM-OLS and D-OLS. Both procedures require estimates of long-run variances, which
are based on the OLS residuals. For long-run variance estimation in our analysis, we use the
Bartlett kernel in conjunction with the data-dependent bandwidth rule of Newey and West
(1994). Furthermore, lead and lag choices are according to Choi and Kurozumi (2012). As a
benchmark, we include in addition the OLS estimator.
Starting the discussion with the estimation results for aluminum (for Japan and Switzer-
land), we find significantly positive coefficient estimates for β1 and significantly negative es-
timates for β2 in case of Japan, indicating an inverted-U shape (Table 4). While the estimates
do not differ strongly across methods, for Japan, the estimated MKC curves and fitted values,
given in Figure A1, show a much better adjustment on the basis of FM-OLS than based on
D-OLS. For Switzerland, the coefficient estimate for β2 is not significantly different from zero.
This leads to large GDP per capita values of the turning points, notably for the OLS and the
D-OLS estimates.
For lead, we find inverted U-shaped relationships for all four considered countries Aus-
tralia, France, Germany, and Switzerland (see Figure A2). Again, all per-capita GDP values of
4Similar extensions of the IM-OLS principle are currently investigated.
9
Table 4: Estimation Results for Aluminum
δˆ t-values βˆ1 t-values βˆ2 t-values exp
(−βˆ1/2βˆ2)
Japan
OLS 0.039 (4.61) 17.976 (7.88) -1.021 (-7.46) 6,657.6
D-OLS 0.061 (10.32) 19.872 (13.09) -1.161 (-13.45) 5,200.8
FM-OLS 0.042 (4.86) 20.524 (9.79) -1.173 (-9.77) 6,296.3
Switzerland
OLS 0.004 (0.50) 1.453 (0.44) -0.041 (-0.21) 4.176×107
D-OLS 0.004 (0.46) 1.453 (0.36) -0.041 (-0.18) 4.176×107
FM-OLS 0.006 (0.79) 4.150 (0.10) -0.191 (-0.81) 51,469.7
the turning points are within sample, with the exception of Germany and the FM-OLS estima-
tor (see Table 5). Finally, in qualitative terms, the results for zinc for France, Germany, Italy
and Switzerland are similar to those for aluminum and lead. As shown in Table 6, all coeffi-
cient estimates exhibit the expected signs and are significantly different from zero, except for
Germany (FM-OLS and D-OLS).
Table 5: Estimation Results for Lead
δˆ t-values βˆ1 t-values βˆ2 t-values exp
(−βˆ1/2βˆ2)
Australia
OLS 0.016 (2.97) 23.837 (8.87) -1.390 (-9.82) 5,279.4
D-OLS 0.023 (3.38) 22.287 (6.46) -1.325 (-7.59) 4,503.5
FM-OLS 0.019 (3.47) 23.718 (8.78) -1.391 (-9.99) 5,043.3
France
OLS -0.033 (-4.86) 9.103 (3.72) -0.460 (-3.67) 19,693.7
D-OLS -0.034 (-8.48) 8.711 (4.56) -0.437 (-4.11) 21,459.2
FM-OLS -0.033 (-8.58) 8.049 (4.55) -0.402 (-4.06) 22,367.5
Germany
OLS -0.023 (-9.23) 6.587 (3.02) -0.340 (-2.75) 16,209.5
D-OLS -0.023 (-6.82) 5.601 (2.96) -0.287 (-2.69) 17,311.4
FM-OLS -0.026 (-9.17) 4.072 (2.69) -0.191 (-2.22) 42,613.1
Switzerland
OLS -0.035 (-2.26) 19.565 (4.48) -1.024 (-3.81) 14,121.9
D-OLS -0.035 (-3.01) 22.328 (4.82) -1.176 (-4.58) 13,322.1
FM-OLS -0.030 (-2.55) 20.425 (4.52) -1.086 (-4.31) 12,129.0
In sum, we find a cointegrating MKC relationship for only a subset of countries. For all
countries and metals with the exception of aluminum for Switzerland βˆ2 is significantly nega-
tive implying an inverted U-shape. For given combination of country and metal furthermore
the estimates do not differ strongly across methods. However, the individual estimates of the
slope parameters differ across countries, in line with the evidence for heterogeneity visible
in Figures 1–3; remarked upon already at the end of Section 2. This implies that estimation
methods that assume parameter homogeneity across countries, such as panel data estimation
methods, should be used with great care, if at all.
10
Table 6: Estimation Results for Zinc
δˆ t-values βˆ1 t-values βˆ2 t-values exp
(−βˆ1/2βˆ2)
France
OLS -0.022 (-4.91) 10.819 (6.13) -0.573 (-6.20) 12,504.3
D-OLS -0.023 (-7.16) 10.735 (7.29) -0.567 (-6.95) 12,951.3
FM-OLS -0.022 (-7.73) 10.069 (7.90) -0.532 (-7.45) 12,904.7
Germany
OLS -0.023 (-7.46) 4.793 (3.73) -0.229 (-3.03) 34,325.1
D-OLS -0.023 (-6.30) 2.624 (1.27) -0.110 (-0.95) 144,565.1
FM-OLS -0.024 (-7.14) 2.606 (1.46) -0.105 (-1.04) 243,419.0
Italy
OLS 0.002 (0.21) 11.373 (4.77) -0.620 (-5.06) 9,674.3
D-OLS 0.013 (2.12) 5.895 (2.29) -0.334 (-2.35) 6,892.6
FM-OLS 0.008 (1.31) 10.025 (4.54) -0.557 (-4.51) 8,129.4
Switzerland
OLS -0.016 (-1.22) 22.852 (2.73) -1.203 (-2.54) 13,354.2
D-OLS -0.013 (-0.86) 23.684 (2.43) -1.256 (-2.28) 12,471.4
FM-OLS -0.017 (-1.62) 22.546 (3.19) -1.185 (-2.99) 13,493.1
4 Summary and Conclusions
Using consumption data for aluminum, lead, and zinc spanning from about 1900 to 2006,
this paper has examined the MKC hypothesis for eight OECD countries, including highly in-
dustrialized countries such as the US, Japan, and Germany. Since the logarithm of GDP per
capita is found to be an I(1) process for the countries under scrutiny, we individually test for
each country whether there is a cointegrating polynomial relationship between the logarithm
of the intensity of metal use and the logarithm of GDP per capita, as well as its square. Based
on the tests for (non-)linear cointegration introduced by Wagner (2013) and Wagner and Hong
(2016), we find support for a cointegrating MKC relationship only for a subset of these coun-
tries, such as Japan and Switzerland in case of aluminum. Similar to the findings originating
from empirical EKC analyses, e.g. by Wagner (2015), we find that the MKC hypothesis is less
strongly supported by the data than when employing standard tests developed for linear coin-
tegrating relationships.
The reduced-form approach pursued here (given by Equation 1) is only a first step to ana-
lyze the MKC hypothesis. To obtain more insights into the relationship between the intensity
of use and GDP per capita, more general specifications and the inclusion of further relevant
economic explanatory variables are necessary. Changes of relative metal prices, for instance,
can be expected to impact the intensity of metal use via substitution effects (see, e.g., Stuermer,
2016). However, as relative metal prices are often found to be stationary, rather than inte-
grated, the employed estimation and testing techniques have to be extended to accommodate
11
also stationary regressors. Furthermore, the presence of relevant substitution effects hints at
the usefulness of system estimation considering several metals jointly. These extensions are,
however, beyond the scope of the present paper.
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Appendix
Table A.1: Continued Overview on Selected Recent Studies on the MKC Hypothesis
Metal Countries Time Support of
Period MKC Hypothesis
Bringezu et al. (2004) Direct material input 26 countries and
EU-15
1960-2000 Yes
Canas et al. (2003) Direct material input 16 industrialized
countries
1960-1998 Yes
Crompton (2015) Steel 26 OECD countries 1970-2012 Yes
Focacci (2005) Aluminum, copper,
lead, nickel, tin, zinc
5 industrialized
countries
1960-1995 No
Guzma´n et al. (2005) Copper Japan 1960-2000 Yes
Huh (2011) Steel South Korea 1975-2008 Yes
Jaunky (2012) Aluminum 20 high-income
countries
1970-2009 Yes
Jaunky (2013) Copper 16 rich countries 1966-2010 Yes
Wa˚rell (2014) Steel 61 countries 1970-2011 Only for
middle-income
countries
Table A.2: Data Range for the Countries under Scrutiny
Country GDP Aluminum Lead Zinc
Australia 1900-2006 1920-2006 1900-2006 1911-2006
France 1900-2006 1900-2006 1900-2006 1900-2006
Germany 1900-2006 1920-2006 1900-2006 1900-2006
Italy 1900-2006 1908-2006 1900-2006 1900-2006
Japan 1900-2006 1911-2006 1900-2006 1911-2006
Switzerland 1900-2006 1920-2006 1900-2006 1927-2006
UK 1900-2006 1900-2006 1900-2006 1900-2006
USA 1900-2006 1900-2006 1900-2006 1900-2006
15
Table A.3: Results of the PO Non-Cointegration Test of Phillips and Ouliaris (1990) and the Cointegra-
tion Test of Shin (1994)
Aluminum Lead Zinc
PO Shin PO Shin PO Shin
Australia -5.87** 0.10* -5.52** 0.05 -3.11 0.09*
France -3.93* 0.07 -4.78** 0.06 -4.29** 0.05
Germany -6.62** 0.09* -5.43** 0.08 -6.31** 0.06
Italy -4.30** 0.08* -4.22** 0.04 -6.04** 0.05
Japan -4.28** 0.07 -3.76 0.13** -6.17** 0.06
Switzerland -6.24** 0.06 -5.72** 0.06 -6.14** 0.06
USA -3.44 0.12** -4.69** 0.31** -5.18** 0.26**
United Kingdom -3.26 0.11** -3.62 0.05 -4.32** 0.06
Note: Bartlett kernel and Newey and West (1994) bandwidth for long-run covariance estimation. Numbers with one asterisk
denote rejection of the null hypothesis at the 10% significance level and numbers with two asterisks indicate rejection of the
null at the 5% significance level.
7 7.5 8 8.5 9 9.5 10 10.5
−6
−5
−4
−3
−2
−1
0
1
ln(GDP)
ln
(IO
U_
Alu
mi
nu
m)
Japan
1900 1920 1940 1960 1980 2000
−6
−5
−4
−3
−2
−1
0
1
ln
(IO
U_
Alu
mi
nu
m)
Japan
8 8.5 9 9.5 10 10.5
−2
−1.5
−1
−0.5
0
0.5
ln(GDP)
ln
(IO
U_
Alu
mi
nu
m)
Switzerland
1900 1920 1940 1960 1980 2000
−2
−1.5
−1
−0.5
0
0.5
ln
(IO
U_
Alu
mi
nu
m)
Switzerland
Figure A1: Estimated aluminum MKC curves and fitted values plots for Japan and Switzerland. On the
left-hand side the dots show the pairs of observations of log GDP per capita and log intensity
of use. The curves show a line that is the result of inserting equidistantly spaced points from
the sample range of log GDP per capita, with corresponding values of the trend given by
t = 1, . . . , T, in the estimated relationship (1) using the coefficient estimates obtained by
FM-OLS (solid – blue) and D-OLS (dotted – red). The right-hand side shows the actual log
intensity of use values (dashed – black) together with fitted values obtained by FM-OLS
(solid – blue) and D-OLS (dotted – red).
16
8 8.5 9 9.5 10 10.5
−3
−2.5
−2
−1.5
−1
−0.5
0
0.5
ln(GDP)
ln
(IO
U_
Le
ad
)
Australia
1900 1920 1940 1960 1980 2000
−3
−2.5
−2
−1.5
−1
−0.5
0
0.5
ln
(IO
U_
Le
ad
)
Australia
7.5 8 8.5 9 9.5 10
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
0
ln(GDP)
ln
(IO
U_
Le
ad
)
France
1900 1920 1940 1960 1980 2000
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
0
ln
(IO
U_
Le
ad
)
France
7.5 8 8.5 9 9.5 10
−1.8
−1.6
−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
ln(GDP)
ln
(IO
U_
Le
ad
)
Germany
1900 1920 1940 1960 1980 2000
−1.8
−1.6
−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
ln
(IO
U_
Le
ad
)
Germany
8 8.5 9 9.5 10 10.5
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
ln(GDP)
ln
(IO
U_
Le
ad
)
Switzerland
1900 1920 1940 1960 1980 2000
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
ln
(IO
U_
Le
ad
)
Switzerland
Figure A2: Estimated lead MKC curves and fitted values plots for Australia, France, Germany and
Switzerland. For further explanations, see Figure A1.
17
7.5 8 8.5 9 9.5 10
−2.5
−2
−1.5
−1
−0.5
0
ln(GDP)
ln
(IO
U_
Zin
c)
France
1900 1920 1940 1960 1980 2000
−2.5
−2
−1.5
−1
−0.5
0
ln
(IO
U_
Zin
c)
France
7.5 8 8.5 9 9.5 10
−3
−2.5
−2
−1.5
−1
−0.5
0
0.5
ln(GDP)
ln
(IO
U_
Zin
c)
Germany
1900 1920 1940 1960 1980 2000
−3
−2.5
−2
−1.5
−1
−0.5
0
0.5
ln
(IO
U_
Zin
c)
Germany
7 7.5 8 8.5 9 9.5 10
−5
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
ln(GDP)
ln
(IO
U_
Zin
c)
Italy
1900 1920 1940 1960 1980 2000
−5
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
ln
(IO
U_
Zin
c)
Italy
8.6 8.8 9 9.2 9.4 9.6 9.8 10 10.2
−3
−2.5
−2
−1.5
−1
−0.5
ln(GDP)
ln
(IO
U_
Zin
c)
Switzerland
1900 1920 1940 1960 1980 2000
−3
−2.5
−2
−1.5
−1
−0.5
ln
(IO
U_
Zin
c)
Switzerland
Figure A3: Estimated zinc MKC curves and fitted values plots for France, Germany, Italy and Switzer-
land. For further explanations, see Figure A1.
18